In a period of 20 years, from 1990 to 2010, it was found that matrix orthogonal polynomials (MOP) satisfy, in some cases, properties as do the classical orthogonal polynomials.
Let us mention, for example, that for matrix versions of Laguerre, Hermite and Jacobi polynomials, i.e., the scalar-type Rodrigues' formula [1]}, [2]} and a second order differential equation [3]}, [4]}, [5]} has been discussed. It also has been proven [6]} that operators of the form
\(D\) =\({\partial }^{2}F_{2}(t)\) +\({\partial }^{1}F_{1}(t)\) +\({\partial }^{0}F_{0}\)  have as eigenfunctions different infinite families of MOP's. A new family of MOP's satisfying second order differential equations whose coefficients do not behave asymptotically as the identity
matrix was found in [3]}; see also [8]}.
We have studied [9]}, [10]} matrix extensions of the generalized polynomials studied in [11]}, [12]}.
Recently, in [13]}, the Christoffel transformation to m,atrix orthogonal polynomials in the real line (MOPRL)
have extended to obtaining a new matrix Christoffel formula, and in [14]}, [15]} more general transformations –of Geronimus and Uvarov type– where also considered.
